Optimal Linear Filter Research Articles

Recursive linear optimal filter for Markovian jump linear systems with multi-step correlated noises and multiplicative random parameters

ABSTRACTThis paper presents the state estimation problem for discrete-time Markovian jump linear systems with multi-step correlated additive noises and multiplicative random parameters (termed as MCNMP). A recursive linear optimal filter for the considered MCNMP (which is abbreviated as RLMMF) is derived based on state augmentation between the original state and mode uncertainty, with the help of estimating the multi-step correlated additive noises online simultaneously. A maneuvering target tracking example under one-step and two-step correlated additive noises scenarios with different cases (i.e. Gaussian/Gaussian mixture distribution and no multiplicative noises) is simulated to validate the designed filter.

Optimal linear filtering for networked control systems with time-correlated fading channels

In this paper, the problem of filtering for discrete-time networked control systems with time-correlated fading channels is considered where each time-correlated fading channel is described by a one-dimensional discrete-time uncertain linear system model with random disturbance. Using the innovation analysis approach and optimal estimates for the products of channel gain and system state obtained, an optimal linear recursive filter is proposed, that has time-independent complexity, and does not increase computation and storage load with time. An example and simulation are provided to show the effectiveness and potential of the proposed new design technique.

The unsupervised optimum linear finite length filter for fourth order wide sense stationary single output systems

The finite length absolute minimum vectors of the Constant Modulus (CM) criterion with an arbitrary source and a single output linear regression model are shown to equal the Wiener filter or one of its phase shifted versions. The exact equations for these vectors are also provided and depend on the second and the fourth order statistical moments of the sample sequence only. These expressions describe the behavior of the Constant Modulus Algorithm (CMA) when it operates at the desired global minimum and expose key characteristics of the CM minimization approach. These characteristics include the existence conditions, the persistency of excitation, the computational complexity, the excess CM cost, the robustness to an additive noise, and the tolerance to the length variations. Moreover, several computer simulation experiments are included to validate our findings.

Optimal Sequential Fusion Estimation With Stochastic Parameter Perturbations, Fading Measurements, and Correlated Noises

This paper focuses on the linear optimal recursive sequential fusion filter design for multisensor systems subject to stochastic parameter perturbations, fading measurements, and correlated noises. The stochastic parameter perturbations existing in the state model are described by white multiplicative noises. The fading measurement phenomena for different sensors are described by independent random variables with known statistical properties. Moreover, the measurement noises of different sensors are correlated with each other and also correlated with the system noise at the same time step. First, a model equivalent to the original system is established by transferring the multiplicative noises into the additive noises. Then, based on the equivalent model and an innovation analysis method, a sequential fusion filter in the linear minimum variance sense is proposed to solve the linear optimal state estimation problem in real time according to the arriving order of measurements from different sensors. Finally, the equivalence on estimation accuracy of the proposed sequential fusion filter and the centralized fusion filter is strictly proven, which shows the optimality of the proposed sequential fusion algorithm. Moreover, the proposed sequential fusion filter has a reduced computational burden. Compared with the distributed matrix-weighted fusion filter, the computation of cross-covariance matrices is avoided and the estimation accuracy is improved. Finally, a simulation example verifies the effectiveness of the proposed sequential fusion filtering algorithm.

Methodology and performance comparison of statistical learning pulse shape classifiers as demonstrated with organic liquid scintillator

In this paper, we present novel methods for automated pulse shape discrimination. The classifiers are trained using simple radionuclide sources and do not require ground truth labeling. We test their performance using labels derived from time of flight experiments and present the results in terms of energy-dependent Receiver Operating Characteristic (ROC) curves. In addition, we also train and test standard pulse shape discrimination methods on the same data for comparison. We find multiple methods that can yield similar false neutron and true neutron rates at 24keVee as tail-to-total or Gatti’s optimal linear filter yield at 54keVee.

Singular value decomposition based impulsive noise reduction in multi-frequency phase-sensitive demodulation of electrical impedance tomography.

As an important means in electrical impedance tomography (EIT), multi-frequency phase-sensitive demodulation (PSD) can be viewed as a matched filter for measurement signals and as an optimal linear filter in the case of Gaussian-type noise. However, the additive noise usually possesses impulsive noise characteristics, so it is a challenging task to reduce the impulsive noise in multi-frequency PSD effectively. In this paper, an approach for impulsive noise reduction in multi-frequency PSD of EIT is presented. Instead of linear filters, a singular value decomposition filter is employed as the pre-stage filtering module prior to PSD, which has advantages of zero phase shift, little distortion, and a high signal-to-noise ratio (SNR) in digital signal processing. Simulation and experimental results demonstrated that the proposed method can effectively eliminate the influence of impulsive noise in multi-frequency PSD, and it was capable of achieving a higher SNR and smaller demodulation error.

Accurate detection of speech auditory brainstem responses using a spectral feature-based ANN method

Abstract The speech auditory brainstem response (sABR) is a promising tool that can be used for objectively assessing auditory function. The main problem in obtaining the sABR is the high background noise, especially noise associated with general brain activity. In practice, a very long recording is needed to detect the sABR. We therefore propose a new detection method of the sABR based on spectral feature extraction that will reduce the detection time without reducing the accuracy. This method involves a constructed feature-frequency vector fed to an artificial neural network. The performance of the proposed method is compared to four other methods reported in the literature: optimal linear filtering, online estimator, Mutual Information, and artificial neural network based on discrete wavelet transforms and approximate entropy. All the methods were evaluated with several datasets of recorded and simulated sABRs ranging from extremely noisy to relatively clean. The proposed method performed very well in terms of sensitivity, specificity, and overall accuracy in detecting the sABR, compared with the other methods The reduction in the required recording time promises to facilitate the application of this measurement technique in clinical settings.

A general packet dropout compensation framework for optimal prior filter of networked multi-sensor systems

This paper proposes a new packet dropout compensation framework for networked multi-sensor systems. It is more general, which includes the existing popular mechanisms such as the zero-input and hold-input mechanisms as the special cases. Based on the proposed compensation framework, the centralized fusion linear optimal full-order prior filters with compensators of different weighting factors are presented. However, it is well known that centralized fusion prior filters (CFPFs) have poor reliability. To improve the reliability, the distributed fusion prior filters (DFPFs) are also given based on the well-known matrix-weighted fusion estimation algorithm in the linear unbiased minimum variance (LUMV) sense. Moreover, the stability and steady-state property of the proposed CFPFs and DFPFs are analyzed. A numerical example is used to make the performance comparisons of the proposed and the existing compensation mechanisms. The simulation results verify the effectiveness of the proposed compensation framework and the corresponding fusion filters.

Blind multi-frame deconvolution by tangential iterative projections (TIP)

A methodology for retrieving the unknown object distribution and point-spread functions (PSFs) from a set of images acquired in the presence of temporal phase aberrations is presented in this paper. The method works by finding optimal complimentary linear filters for multi-frame deconvolution. The algorithm uses undemanding computational operations and few a priori, making it simple, fast and robust even at low signal-to-noise ratios. Results of numerical simulations and experimental tests are given as empirical proof, alongside comparisons with other algorithms found in the literature.

Optimal linear filtering design for discrete‐time systems with cross‐correlated stochastic parameter matrices and noises

This study investigates the design of an optimal linear estimator for a class of discrete-time linear systems with correlated stochastic parameter matrices and noises. The considered systems are endowed with the following two main features: (i) cross-correlated stochastic matrices involved in the state and observation equations are assumed and (ii) the process and observation noises have cross-correlation at the same time instant. A decorrelation framework is established to reconstruct such systems. With the equivalent transformation of original dynamic systems resulting from decorrelating operations, the optimal linear recursive filter in the minimum mean square error sense is developed by employing the results of Kalman filtering. The discrete-time linear systems with multiple packet dropouts are modelled as a particular case, and then the proposed filter is applied directly to estimate the system state, while a comparative analysis between the new method and the existing approaches is provided. Simulations demonstrate the effectiveness of the presented algorithm.

Optimal experimental design in the context of canonical expansions

In a wide variety of engineering applications, the mathematical model cannot be fully identified. Therefore, one would like to construct robust operators (filters, classifiers, controllers etc.) that perform optimally relative to incomplete knowledge. Improving model identification through determining unknown parameters can enhance the performance of robust operators. One would like to perform the experiment that provides the most information relative to the engineering objective. The authors present an experimental design framework for parameter estimation in signal processing when the random process model is in the form of canonical expansions. The proposed experimental design is based on the concept of the mean objective cost of uncertainty, which quantifies model uncertainty by taking into account the performance degradation of the designed operator owing to the presence of uncertainty. They provide the general framework for experimental design in the context of canonical expansions and solve it for two major signal processing problems: optimal linear filtering and signal detection.

Characterization of Quadratic Nonlinearity between Motion Artifact and Acceleration Data and its Application to Heartbeat Rate Estimation.

Accelerometers are applied to various applications to collect information about movements of other sensors deployed at diverse fields ranging from underwater area to human body. In this study, we try to characterize the nonlinear relationship between motion artifact and acceleration data. The cross bicoherence test and the Volterra filter are used as the approaches to detection and modeling. We use the cross bicoherence test to directly detect in the frequency domain and we indirectly identify the nonlinear relationship by improving the performance of eliminating motion artifact in heartbeat rate estimation using a nonlinear filter, the second-order Volterra filter. In the experiments, significant bicoherence values are observed through the cross bicoherence test between the photoplethysmogram (PPG) signal contaminated with motion artifact and the acceleration sensor data. It is observed that for each dataset, the heartbeat rate estimation based on the Volterra filter is superior to that of the linear filter in terms of average absolute error. Furthermore, the leave one out cross-validation (LOOCV) is employed to develop an optimal structure of the Volterra filter for the total datasets. Due to lack of data, the developed Volterra filter does not demonstrate significant difference from the optimal linear filter in terms of t-test. Through this study, it can be concluded that motion artifact may have a quadaratical relationship with acceleration data in terms of bicoherence and more experimental data are required for developing a robust and efficient model for the relationship.

Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems

Optimization of the stability of synchronized states between a pair of symmetrically coupled reaction-diffusion systems exhibiting rhythmic spatiotemporal patterns is studied in the framework of the phase reduction theory. The optimal linear filter that maximizes the linear stability of the in-phase synchronized state is derived for the case in which the two systems are nonlocally coupled. The optimal nonlinear interaction function that theoretically gives the largest linear stability of the in-phase synchronized state is also derived. The theory is illustrated by using typical rhythmic patterns in FitzHugh-Nagumo systems as examples.

Limited memory optimal filter for discrete-time systems with measurement delay

This paper considers the limited memory optimal filter for discrete-time systems with measurement delay. Firstly, we deal with the measurement delay using the reorganized innovation analysis approach. According to the projection theory, an optimal linear filter is provided in the linear minimum mean square error (LMMSE) sense. With the increase of time, the size of LMMSE filter problem will grow. Then, in order to avoid this problem, we explore a limited memory optimal filter calculated by applying the recent N measurements. Finally, we give a numerical example to show that the limited memory optimal filter is effective.

High-Order Filtering of LIDAR Data to Assist Coal Shiploading

A high-order signal model is proposed in which the states are Kronecker tensor products of probability distributions. This model enables an optimal linear filter to be specified. A minimum residual error variance criterion may be used to select the number of discretizations and Kronecker products. The filtering of LIDAR data from a coal shiploader environment is investigated. It is demonstrated that the proposed method can outperform conventional Kalman and hidden Markov model filters.

Feedback quadratic filtering

This paper concerns the state estimation problem for linear discrete-time non-Gaussian systems. It is known that filters based on quadratic functions of the measurements processes (Quadratic Filter) improve the estimation accuracy of the optimal linear filter. In order to enlarge the class of systems, which can be processed by a Quadratic Filter, we rewrite the system model by introducing an output injection term. The resulting filter, named the Feedback Quadratic Filter, can be applied also to non asymptotically stable systems. We prove that the performance of the Feedback Quadratic Filter depends on the gain parameter of the output term, which can be chosen so that the estimation error is always less than or equal to the Quadratic Filter.

Modeling a One-Dimensional Markov Random Walk Between Reflecting Baffles

An algorithm is proposed for calculating the autocorrelation function of a Markov sequence with a limited range of possible increments for constructing an optimal linear filter. Results from the modeling program are presented.

Helical reconstruction in RELION.

We describe a new implementation for the reconstruction of helical assemblies in the empirical Bayesian framework of RELION. Our approach calculates optimal linear filters for the 3D reconstruction by embedding helical symmetry operators in Fourier-space, and deals with deviations from perfect helical symmetry through Gaussian-shaped priors on the orientations of individual segments. By incorporating our approach into the standard pipeline for single-particle analysis in RELION, our implementation aims to be easily accessible for non-experienced users. Although our implementation does not solve the problem that grossly incorrect structures can be obtained when the wrong helical symmetry is imposed, we show for four different test cases that it is capable of reconstructing structures to near-atomic resolution.

Linear optimal filter for system subject to random delay and packet dropout

SummaryThis note is concerned with the linear estimation problems for discrete‐time systems where the measurements are subject to random time delay and packet dropout. Different from most of previous works, the time‐stamping is assumed to be unavailable in this paper. In this case, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time‐stamping, a new observation is introduced by the summation of all the measurements received in the same time. Then, the random time delay measurement system is converted into a constant‐delay measurement system with multiplicative noises where the noise is binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by using the transformation of auto‐regressive moving average model to state‐space model and the standard Kalman filtering. The convergence and stability of the filter are also analyzed. A simulation example is given to show the effectiveness of the proposed estimator. Copyright © 2016 John Wiley & Sons, Ltd.

An adaptive sequential estimation algorithm for velocity jamming suppression

In this paper, we consider the moving target detection problem for a Pulse Doppler (PD) radar in the presence of multiple velocity jamming. Exploiting the observation that the repeater jamming often contaminates more than one radar pulse, we present an adaptive sequential estimation algorithm to obtain simultaneously the target and jamming profiles in the Doppler domain. At each iteration, employing the estimated Doppler profiles of targets and jamming obtained at the previous iteration, the optimal linear filters are designed to minimize the output average power for each Doppler bin. The presented sequential estimation algorithm yields very low Doppler side lobes and the jamming velocities are eliminated in the Doppler profiles of targets. Finally, we evaluate the performance of the proposed technique as well as the Matched Filter (MF) method via numerical simulations.